Modified Allocation Model Results
The results of the modified allocation model (to determine the proportion of an investor's portfolio that should be invested in WIND) described in my previous note are presented below.
Notes:
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W = WIND
W2 = another stock whose return/probability profile is identical to WIND but whose performance is totally independent of WIND's.
A = and alternative stock with a different return/probability function (less risk but less upside potential)
B = balance of the portfolio returning 25% with certainty during the period.
I = initial total portfolio = 1,000,000 - to keep the numbers simple.
Each proportion is tested with 600 trial simulations, with the following results displayed:
Avge - the average utility value of the portfolio
Min - the lowest utility value of the portfolio, from the 600 simulations
10% - the portfolio utility value at the 10% confidence level (i.e. 10% of the simulations have a lower utility value)
50% - the portfolio utility value at the 50% confidence limit (i.e. the median)
90% - the portfolio utility value at the 90% confidence limit
Max - the utility value of the portfolio produced from the highest simulation.
Selection Criteria:
Min - must be greater than or equal to 0. (Remember: this translates to a portfolio of at least 500,000)
10% - must be greater than or equal to 1,000,000
Results:
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--------------------------- Initial ----------------------------------------
Proportions
1 2 3 4 5
W 60% 30% 30% 40% 30%
W2 0% 0% 30% 0% 0%
A 0% 0% 0% 45% 70%
B 40% 70% 40% 15% 0%
Avge 1,793,361 1,537,674 1,856,355 1,714,846 1,639,773
Min 1,168 844,987 243,656 188,734 311,175
10% 714,667 1,007,415 1,059,370 1,041,372 1,087,815
50% 1,841,425 1,539,086 1,898,227 1,726,280 1,658,142
90% 2,830,442 2,058,084 2,588,052 2,414,088 2,225,391
Max 3,049,333 2,185,405 3,021,426 2,700,177 2,535,501
Comments:
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1. Column 1 shows the results of the the type of allocation advocated by Prof. Benn's model. It clearly does not pass our 10% criteria.
2.. With only W and B available, the maximum that can be allocated to W that would meet our criteria seems to be around 30%. This is shown in column 2. Further testing (not reported here) shows that any higher allocation jeopardizes at least one of the criteria
3. Interestingly, if you could find another stock W2 with the same performance characteristics as WIND, but which moves totally independent to WIND (this is important), then one would be justified in putting 30% each in W and W2, as shown in column 3, with the same kind of upside potential as in column 1 but with a much better downside. In column 3, if either W or W2 is increased to more than 33, the selection criteria are no longer met.
4. If W2 does not exist and you had to settle for another stock A instead, columns 4 and 5 show the kind of combinations that would satisfy our criteria.
5. The conclusion is that it would be inadvisable to invest more than 30% of one's portfolio in WIND. However, if you are able to find a second stock B, and perhaps a third, fourth, etc..., this can in fact help to increase your allocation for WIND.
Any comments on the above results would be most appreciated.
Erwin
PS - Sorry - the above jumble of numbers is supposed to be a six column table with the left column containing labels and 5 columns of results. Obviously tables don't transport well into the SI editor. I will re-submit the results in a more legible fashion. |
